Mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder

The steady mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder in a stream flowing vertically upwards is numerically studied for both cases of heated and cooled cylinders. The governing partial differential equations are transformed into dimensionless forms using an appropriate transformation and then solved numerically using the Keller-box method. The comparison between the solutions obtained and those for a Newtonian fluid is found to be very good. Effects of the mixed convection and elasticity parameters on the skin friction and heat transfer coefficients for a fluid having the Prandtl number equal to one are also discussed. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point. However, for a sufficiently cold cylinder there will not be a boundary layer.     

Two-dimensional problem of a uniform flow of a two-layer fluid of finite depth past a circular cylinder

The linear steady problem of an irrotational uniform flow past a horizontal circular cylinder located in the upper or in the lower layer of a two-layer fluid is solved by the multipole-expansion method. The flow is perpendicular to the axis of the cylinder. The fluid is assumed to be inviscid and incompressible, and the flow in each layer is assumed to be potential. The upper layer can be bounded by a free surface or a solid lid, and the lower layer by a rigid horizontal bottom. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 91–101, November–December, 1998.     

Perturbations on interfaces between media driven by the vertical ascent of a circular cylinder in a multilayer fluid

The initial-boundary value problem of the vertical ascent of a circular cylinder in a multilayer fluid is considered within the nonlinear theory. In each layer the fluid is ideal, incompressible, heavy, and homogeneous. At the initial instant of time the cylinder is located in the lower layer and begins smoothly to accelerate vertically from zero to a constant velocity. A system of integrodifferential equations of the problem is obtained. As unknowns, this system contains both the intensities of the singularities simulating the fluid and rigid boundaries and the functions describing the shape of the interface between the fluid media. The numerical solution of this system is based on two iteration processes, one of which is associated with time integration using the Runge-Kutta-Felberg scheme, while the other is associated with the solution of a system of linear algebraic equations obtained by discretization of the integral relations in each time step. The problem of the vertical ascent of a cylinder in a three-layer fluid (seawater, fresh water and air) is considered in detail. The results of calculating the perturbations of the fluid interfaces and the distributed and total hydrodynamic contour characteristics are given. The results obtained are compared with the solution of the problem of the ascent of a circular cylinder to the interface between water and air media. It is concluded that the third layer and the Froude number significantly affect the nature of the perturbations induced by the contour. Omsk, e-mail: gorlov@iitam.omsk.net.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–159, March–April, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

Oscillations of a cylinder piercing a linearly stratified fluid layer

The plane problem of the small steady-state oscillations of a horizontal cylinder arbitrarily located in a three-layer fluid whose upper and lower layers are homogeneous and whose middle layer is linearly stratified is considered in the linear formulation using the Boussinesq approximation. The fluid is assumed to be ideal and incompressible. The method of mass sources distributed along the body contour is used in the internal wave generation regime and an integral equation for the fluid pressure is derived in the non-wave regime. The hydrodynamic load acting on the body is calculated as a function of the oscillation frequency of the cylinder and its location. The results are compared with experimental data.     

Constant heat flux solution for mixed convection boundary layer viscoelastic fluid

The mixed convection boundary layer of a viscoelastic fluid past a circular cylinder with constant heat flux is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results obtained in the form of velocity distributions and temperature profiles are presented for a range of values of the dimensionless viscoelastic fluid parameter. It is found that for some values of the viscoelastic parameter and some negative values of the mixed convection parameter (opposing flow) the momentum boundary layer separates from the cylinder. Heating the cylinder delays separation and can, if the cylinder is warm enough, suppress the separation completely. Similar to the case of a Newtonian fluid, cooling the cylinder brings the separation point nearer to the lower stagnation point.     

Dynamics of a Fluid in a Rotating Horizontal Cylinder

The behavior of a low-viscosity fluid in a rotating horizontal circular cylinder is investigated experimentally. The stability of the centrifuged layer, the motion of the fluid with respect to the cavity, the excitation of inertial waves on the fluid surface, and the effect of the waves on the stability and flow structure are studied over a wide region of relative occupancy of the cavity. The results are analyzed from the viewpoint of vibrational mechanics in which the motion is generated by the oscillations of the fluid with respect to the cavity and the gravity force plays the role of the force oscillating in the cavity reference system.     

Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall

The flow around a circular cylinder placed close to a horizontal plane wall was investigated experimentally. Fluctuations of lift and drag of the cylinder and wall interference effects were studied in terms of the gap height between the cylinder and wall and the thickness of the turbulent wall boundary layer. The fluctuating fluid forces acting on the cylinder sharply increased, and the regular vortex shedding, i.e. Kárman vortex streets, started to form beyond a critical gap height. The formation of Kárman vortex streets was abruptly interrupted when the bottom of the cylinder came in contact with the outer layer of the boundary layer developed on the wall. This critical gap height correlated well with the thickness of the boundary layer.     

Instability of an Oscillating Cylinder in a Circulation Flow of Ideal Fluid

The problem of the stability of a circular cylinder in a circulation flow is considered under the condition that the cylinder can perform both free (free cylinder) and forced oscillations (cylinder on a spring). It is shown that this simple system can be unstable in the presence of flow vorticity. Particular cases of vorticity distributions which make it possible to obtain an analytic solution are considered. The case of weak monotonically decreasing vorticity of an arbitrary form is analyzed for an arbitrary relation between the densities of the cylinder and the fluid. It turns out that the instability can develop only for a cylinder whose density is greater than that of the fluid. An approximate method of solving this problem based on consideration of the energy balance in the system is constructed. This makes it possible to obtain an expression for the growth rates and explain the physical mechanism realizing the instability, which is associated with the possibility of energy transfer from perturbations in the critical layer to the cylinder oscillations.     

Deformation by the external flow of the surface of a magnetic fluid covering a circular cylinder

As one of the methods of controlling separation of a flow and reducing hydrodynamic resistance in flow round the body, [1] proposes covering the surface of the body with a layer of magnetic fluid maintained by a inhombgeneous field. The effectiveness of the method is studied in the example of flow rounda circular cylinder covered with a uniform layer of a magnetic fluid the surface of which is also assumed to be cylindrical and not dependent on the external flow. The resistance of the cylinder falls (if the viscosity of the magnetic fluid is not too high) and can be greatly reduced. It is of interest to determine the nature of the deformation produced in the surface of the magnetic fluid by the external flow, since the degree to which the boundary can be deformed determines whether the proposed method can be realized in practice. Moreover, the magnitude of the deformation evidently affects the resistance of the cylinder and determines the limits of the applicability of the approximation adopted in [1] for the nondeformed state of the surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 28–31, January–February, 1988.     

Boundary layer on the moving surface of a cylinder

A study is made of the problem of the boundary layer on a cylinder with a moving surface when the cylinder moves with constant velocity in an incompressible fluid. Expressions are obtained for the distributions of the frictional stress on the surface of the cylinder and the coordinate of the singular point in the solution of the boundary layer equations that indicates the appearance of a region of reverse flow for different values of the relative velocity of the motion of the surface of the cylinder. Numerical calculations have been made of the work of the force of friction associated with displacement of the cylinder, the work expended on the motion of its surface, and, in the case of flow separation, the work of the pressure forces (it being assumed here that the pressure and friction on the wall behind the singular point are constant and equal to the pressure and friction at the singular point).     

Measurements of layer depth during baroclinic instability in a two-layer flow

This study investigates the baroclinic instability of a two-layer rotating fluid system. The instability is generated by releasing a cylinder of buoyant fluid at the surface of ambient fluid. The buoyant fluid is dyed so that its depth may be determined from its optical thickness. The system first adjusts until the horizontal density gradient is balanced by a flow along the front, and the adjusted state is then unstable to azimuthal waves. Contours of constant upper layer depth are examined, and the perturbation at each azimuthal wavenumber is determined. The initial wavenumber is well modelled by simple quasi-geostrophic theory. There is a clear high wavenumber cutoff, and a transfer of energy to larger scales with time.     

Very slow flow of Bingham viscoplastic fluid around a circular cylinder

Numerical simulations have been used to study the flow of a Bingham viscoplastic fluid around a circular cylinder in an infinite medium with negligible inertia effects. Papanastasiou's regularisation technique has been adopted to approximate the model. The case corresponding to preponderant plasticity effects has been particularly studied and convergence of the solutions examined in detail. The flow kinematics and stresses have been determined. The rigid zones have been identified and characterised. At large Oldroyd numbers, when plasticity effects become preponderant, a viscoplastic boundary layer appears around the cylinder. The characteristics of this viscoplastic boundary layer are quantified. The results are compared with existing theoretical results, concerning particularly the predictions of the viscoplastic boundary layer theory and the plasticity theory.     

Non-darcy natural convection on a vertical cylinder in a saturated porous medium

The steady free convection boundary layer flow of non-Darcy fluid along an isothermal vertical cylinder embedded in a saturated porous medium using the Ergun model has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme developed by Keller. It is found that the heat transfer is strongly affected by the modified Grashof number which characterizes the non-Darcy fluid, and the curvature parameter. Also the heat transfer is found to be more than that of the flat plate.     

Disturbances, lift and drag forces due to the translation of a horizontal circular cylinder in stratified water

The uniform flow of a fluid with a narrow stratified layer past a horizontal circular cylinder is studied experimentally. This is done through a Galilean transformation of the problem to a situation where the cylinder moves, and the water is at rest. Measurements were made of the interfacial waves formed behind the cylinder towed horizontally at constant speeds. A specially designed stiff force measuring system with a resolution of 0.5 mN measured the drag and lift forces exerted upon the cylinder. When fluid buoyancy forces dominate, it is shown that the increased drag force and other pertinent properties of the problem are efficiently described in terms of a densimetric Froude number, and explicitly independent of the Reynolds number. Lee-waves were detected at all towing speeds less than the speed of long interfacial gravity waves. Maximum wave heights occurred at half of that speed. Vortex shedding was hampered for speeds less than 0.65 of the long interfacial wave speed. Recommended values of increased drag-coefficients are given. The importance of a finite thickness of the stratified layer is documented. The critical densimetric Froude number defining when stratification starts to be important becomes lower with increasing layer thickness. And, with the cylinder located in the stratified layer, the drag-force does not increase although internal waves of appreciable height develop. The situation modelled has its engineering counterpart in the flow past submerged tube bridges.The research presented here is based on parts of my doctoral work carried out during 1988–1990, partially supported by the Norwegian Road Research Laboratory.     

Free circular viscoplastic fluid flow with a hydrolubricant layer in the gap between coaxial cylinders

Free circular viscoplastic fluid flow in the gap between coaxial cylinders with a hydrolubricant layer on the inner cylinder is investigated theoretically. Mathematical models of the velocities and shear stresses for the transported and lubricating fluids in the laminar flow regime are proposed.     

Simulation of transverse self-oscillations for a free circular cylinder mounted with a narrow gap in a plane channel

The experimentally observed self-oscillations of a cylinder mounted with a narrow gap in a plane channel are simulated. The added masses of the cylinder are calculated in the framework of ideal fluid theory by a generalized image method. In order to describe the self-oscillations in a real fluid, some dissipative factors and an impulsive impact force exerted on the cylinder are introduced.     

The interaction of a gravity current with a circular cylinder mounted above a wall: Effect of the gap size

The flow of a gravity current past a circular cylinder mounted above a bottom wall is studied by means of two-dimensional Navier–Stokes simulations. The investigation focuses on the effects of the gap size on the forces acting on the cylinder. The interaction of the current with the cylinder can be divided into an impact, a transient, and a quasisteady stage. During the impact stage, the gravity current meets the cylinder, and the drag increases towards a maximum, while the lift undergoes a drastic fluctuation which increases noticeably with the gap size. During the quasisteady stage, the flow past the cylinder resembles that observed in constant-density boundary layer flows past cylinders: Karman vortex shedding is observed for sufficiently large gap sizes, while a vorticity cancellation mechanism is responsible for the suppression of vortex shedding at small gap sizes. On the other hand, interesting differences that distinguish the gravity current case from the constant-density case are the presence in the gravity current flow of a component of the mean quasisteady lift due to buoyancy, and another component from the deflection of the wake towards the wall by the constriction of the dense fluid flow downstream of the cylinder, as well as the cancellation of vortex shedding for all gap sizes when the ratio of the channel depth to lock height is decreased from 5 to 1.     

A transient natural convection of micropolar fluids over a vertical cylinder

A transient free convective boundary layer flow of micropolar fluids past a semi-infinite cylinder is analysed in the present study. The transformed dimensionless governing equations for the flow, microrotation and heat transfer are solved by using the implicit scheme. For the validation of the current numerical method heat transfer results for a Newtonian fluid case where the vortex viscosity is zero are compared with those available in the existing literature, and an excellent agreement is obtained. The obtained results concerning velocity, microrotation and temperature across the boundary layer are illustrated graphically for different values of various parameters and the dependence of the flow and temperature fields on these parameters is discussed. An increase in the vortex viscosity tends to increase the magnitude of microrotation and thus decreases the peak velocity of fluid flow. An increase in the vortex viscosity in micropolar fluids is shown to decrease the heat transfer rate.     

Asymmetric transient response of a hollow cylinder enclosing a compressible fluid

The asymmetric transient response of a hollow cylinder confining a compressible fluid is analyzed. The cylinder is excited by radial displacement prescribed over a rectangular footprint on the cylinder’s outer surface. The special case of plane-strain is also analyzed. A comparison of dilatational stress in the solid cylinder and fluid pressure in the fluid-filled cylinder reveals how a projectile may decelerate faster in the latter.     

Motion of a circular cylinder in a viscous liquid between parallel plates

The two-dimensional motion of a cylinder in a viscous fluid between two parallel walls of a vertical channel is studied. It is found that when the cylinder moves very closely along one of the channel walls, it always rotates in the direction opposite to that of contact rolling along the nearest wall. When the cylinder is away from the walls, its rotation depends on the Reynolds number of the flow. In this study two numerical methods were used. One is for the unsteady motion of a sedimenting cylinder initially released from a position close to one of the channel walls, where the Navier-Stokes equations are solved for the fluid and Newton's equations of motion are solved for the rigid cylinder. The other method is for the steady flow in which a cylinder is fixed in a uniform flow field where the channel walls are sliding past the cylinder at the speed of the approaching flow, or equivalently a cylinder is moving with a constant velocity in a quiescent fluid. The flow field, the drag, the side force (lift), and the torque experienced by the cylinder are studied in detail. The effects of the cylinder location in the channel, the size of the channel relative to the cylinder diameter, and the Reynolds number of the flow are examined. In the limit when the cylinder is translating very closely along one of the walls, the flow in the gap between the cylinder and the wall is solved analytically using lubrication theory, and the numerical solution in the other region is used to piece together the whole flow field.This research was supported by NSF DMR91-20668 through the Laboratory for Research on the Structure of Matter at the University of Pennsylvania and from the Research Foundation of the University of Pennsylvania.